Here is a proof of Gaussian distribution as a limit of the Poisson distribution https://www.roe.ac.uk/japwww/teaching/astrostats/astrostats2012_part2.pdf
Here is a proof of Gaussian distribution as a limit of the Poisson distribution https://www.roe.ac.uk/japwww/teaching/astrostats/astrostats2012_part2.pdf